My previous post on TelexFree was the result of a quick spreadsheet model that assumed a geometric growth rate that was uniformly assumed for all members. On a recent flight, I built an object oriented model in MATLAB to more realistically show how telex works. This is a really fascinating system.
First, all my code is here on github, but I incorporated the following items:
- A new recruit saturates their ‘warm market’ first (friend and family), but the number of conversations they have decreases to a trickle
- I have no idea what historical conversion rates are, but things blow up when each recruit starts talking to more than 5 people with a probability of success of 0.1 or greater (expected value of 1/2 recruit per month).
There is a lot to talk about here, but I wanted to share the interesting nature of networks you get if you consider a stochastic conversation rate. Here are four plots at different levels of conversion probability:
And after a little more work, I incorporated some more dynamics and ran the model for a simulated year. In particular, now:
- The game stops when the boss has less than 5 weeks of money to pay out
- There is a population saturation of 500 people, after 500 people are recruited, the market doesn’t grow (yes, this should be bigger, but I’m interested in the dynamics that come from the fact that at some point the pool of interested investors is saturated)
- I track cash flow between the members and the owner. I don’t yet include the binary compensation, but that is simple enough to add.
- Payments (the \$20 return) come two weeks after submitting payment.
Here are my results:
You can see that in this scenario, I ran for 52 weeks with a conversion probability of 10% (1 out of ten conversations would be a sale on average). Also, the participants attempt 6 sales the first week, then 5 the next,4,3,2,1 and one for the duration of the model as one’s contacts are exhausted. The end result is 79 winners (or roughly 16%) with an average win of \$109.31. The other 421 individuals lost an average of \$-120.81. The owner walked away with roughly \$42,000. Obviously, each of these could increase, but they would increase proportionally.
If I increase the network growth to a maximum of 5000, the curve starts getting much steeper with a big winner with around \$650, the owner now has \$487,216 (they would have had much more if they wouldn’t have waited until growth stopped). They shut down the operation at the 46th week when their cash flow diminished to 5 weeks of possible payment. As the network grew, the percentage of winners went down to 12% and the losers lost an average of \$-127. However, see how very similar the curve shape is overall. The system behavior is very robust when compared with market size and membership fluctuations.
This didn’t look right to me. I found the growth dynamics to behave way too optimistically. In reality, every movement is driven by zealots who go all in, who motivate and exploit the sheep. I decided to set up a random draw where 10% of new members are zealots. You, the founder, are of course a zealot. Zealots saturate their local network and continue to pitch TelexFree each week. They recruit many non-zealots who have a 50% chance of having a conversation with someone each week. Zealots also buy the AdCentral Family Pack for \$1,375 and earn \$100 back a week from the network. At this point there is huge variance in the model, so I will run three scenarios with the same parameters (52 weeks, 10% chance of completing a sale on average).
See how very differently the three scenarios developed. From a year the boss made either \$2770, or \$8860 or lost \$1360. This seems much more realistic as different individuals are going to have very different experiences, depending how aggressively they recruit and how lucky they are. In the zealot model, few nodes have large downstreams, which means that few individuals profit and not necessarily the earliest members. Also, most losers only lose a modest sum, but they are vast in number. The third scenario is the worst for the owner and that is when an individual goes all in, but fails to recruit other members. The network never gets anywhere and that member never becomes a profitable node. This tells me their strategy is to actively reward growth.
Please post to comments if anyone has dynamics they would like to see in the model.
If I have more time, I would like to better understand the following questions:
- What rate of growth is necessary for profitability and when is the optimal exit strategy for participants and the owner (game theory)?
- What probability of conversion is necessary for growth?
- It looks like their compensation scheme has become more complex. Easy enough to model, but incentivizing growth. See this page.